Multichannel Quantum Defect Theory -The Brief Introduction - Department of Chemistry Kim Ji-Hyun

1.What is a channel ?  Any possible grouping of elementary or composite particles corresponding to a particular final state  Elastic and Inelastic scatterings  Above threshold : open Below threshold : closed

Particles : a, b, c Bound states : (bc), (bc) , (ac) ☞ channel 0, 1, 2, 3 a + (bc) → a + b + c (breakup) → a + (bc) (elastic scattering) → a + (bc)  (excitation) → b + (ac) (rearrangement)

2. Quantum Defect  For a hydrogenic atom, E n = E ∞ - 1/n 2 For an alkaline or alkaline-earth atom, E n = E ∞ – 1/(n –  ) 2 n = n –  : effective quantum number  : quantum defect ☞ from short-range interactions with a core

3. Division of Region ☞ system = ionic core + a Rydberg electron 1) The inner region(R ≤ R 0 ) the existence of strong short-range interactions besides a long-range potential spanned by regular solutions obtained from solving the close-coupled equation

2) The outer region (R ≥ R 0 ) Channels are decoupled. spanned by regular and irregular solutions obtained from solving the ordinary second- order differential equation ※ the most famous base pair ⇒ Coulomb functions

4. Boundary conditions  For standing wave channel basis, the continuity conditions at the matching radius R 0  For fragmentation eigenchannels,  the condition imposing on their asymptotic forms  The divergence terms must disappears in asymptotic regions.

5. The power in experiments  From the compatibility equation, Lu-Fano plot : graphical determination of discrete levels From cross sections, Reproduction of complex spectra with the short-range K matrix and the long-range quantum defect parameters  and 

<References>  Ch. Jungen, Molecular Application of Quantum Defect Theory (Institute of Physics Publishing, Bristol, 1996)  John R. Taylor, Scattering theory(John Wiley & Sons, New York, 1972)  C. –W. Lee, submitted to Phys. Rev. A